Serena Williams celebrates on her way to a fourth-round U.S. Open victory Sunday against Sloane Stephens. / Robert Deutsch, USA TODAY

by USA TODAY Sports, USA TODAY

by USA TODAY Sports, USA TODAY

NEW YORK - For a while, the hyped rematch between Serena Williams and Sloane Stephens was worthy of the buildup.

Then, all of a sudden, it was over.

Williams, who lost to Stephens in the quarterfinals of the Australian Open this year, dominated the second set on the way to a 6-4, 6-1 victory in the fourth round of the U.S. Open.

After she served out the match, in 1 hour, 28 minutes, Williams rushed to the net for what appeared to be a warm handshake. There were smiles from each, the 31-year-old 16-time Grand Slam champ and the 20-year-old rising star.

"Going into the match I definitely wanted to be focused the whole time," Williams said. "That's all I wanted to do. Whether I was going to win or lose, I just wanted to play my game and do well."

Though a fourth-round match, even Williams sensed it was more: "It definitely felt like a really big match, because Sloane is such a great player," Williams said in an on-court interview.

There was big buildup, not only because it was a clash of Americans of different generations at the top of the game but also because of what happened in the weeks after that January upset.

After the Australian Open, a brouhaha erupted over comments Stephens made in a magazine article - calling Williams a phony, among other things. There were un-followings on Twitter. There was a general media feeding frenzy.

Even though Williams, at least publicly, stayed above the fray, there was clear tension leading into the match.

Once it began, there were big serves from both players. There was heavy hitting off the ground. There was leg-churning defense. There were occasional fist pumps and exhortations.

It was still close through 4-4 in the first set. From there, Williams won eight of the last nine games. No. 15 seed Stephens had 29 unforced errors.

"I thought I played good. There were times I played some really good tennis," Stephens said. "Second set got away from me a little bit, but overall I thought I played great."

Stephens, though still looking for her first WTA title, delivered a strong Grand Slam season. She was one of three players, including Williams and No. 3 seed Agnieszka Radwanska, to reach the fourth round in all four majors.

But having Williams on her side of the draw isn't ideal.

"Yeah, it's tough. But everyone has their time to shine," Stephens said. "I think she's obviously No. 1 in the world for a reason.

"Maybe one day when she's not playing people would be, 'Maybe I wish I wasn't on the same side as Sloane' . ... Things happen in their time. It's an honor to be able to play on the court with one of the greatest tennis players of all time."

So what did Williams say when she greeted Stephens at the net?

"I just said, 'Good job.' "

Williams, the defending champion, will face Carla Suarez Navarro of Spain next, and she says there won't be a letdown.

"Absolutely not," Williams said. "I've been at this for a long time, so for me in my career, there are no letdowns. I think (Monday) playing the doubles will definitely help me continue to try to stay in this tournament."